How Long Is the Coastline of Great Britain? Essay

958 Words4 Pages
‘Only truly ‘accurate’ measure of the length of the coastline — any coastline — shows that it is almost infinitely long.’[1] The coastline of Great Britain is difficult to measure because of the methods of measuring them. This report will attempt to find the length of Britain’s coastline using two different methods and discuss the advantages and disadvantages of each method. One method that gives a brief outline of a coastline’s length would be looking at maps of various scales. The result of this would be smaller scale maps resulting in shorter coastline lengths and larger scale maps, longer coastline lengths. This is called the coastline paradox: a term founded by English mathematician Lewis Fry Richardson and means…show more content…
The letter r represents the width of each box and N(r) represents the number of boxes with width r. N(r) can also be described as 1/r. For the box dimension method there is a box dimension formula which uses the laws of logarithms to solve the box dimension of an image. The symbol meaning what happens to the formula as r gets smaller. The next step to is to take log(N(r) and log(1/r) and place them in the table of results and calculate log(N(r) and log(1/r) for each map. The outcome should be this: A graph should then be drawn with log(1/r) along the x axis and log(N(r)) along the y axis. Find an appropriate number to go up in that is suitable to the results table, plot the points and draw a line of best fit, then work out the gradient of the graph (the vertical length divided by the horizontal length of a right angle drawn from two points on the line). The gradient of the graph gives the dimension of Britain’s coastline; 1.01 dimensional. This concludes that Britain’s coastline length is infinite as the dimension is greater than one. Despite knowing the length of Britain’s coastline is infinite, knowing the dimension of it is not of much use. However the ruler method can find an approximate length of the coastline. The method uses straight lines drawn along the perimeter of a coastline on a map, using a specific length. In this case the length will be 2cm. The 2cm should then be deemed equal to a length
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